Cyclic plasticity and shakedown in high-capacity electrodes of lithium-ion batteries

Of all materials, silicon has the highest capacity to store lithium, and is being developed as an electrode for lithium-ion batteries. Upon absorbing a large amount of lithium, the electrode swells greatly, with a volumetric change up to 300%. The swelling is inevitably constrained in practice, often leading to stress and fracture. Evidence has accumulated that the swelling-induced stress can be partially relieved by plastic flow, and that electrodes of small feature sizes can survive many cycles of lithiation and delithiation without fracture. Here we simulate a particle of an electrode subject to cyclic lithiation and delithiation. A recently developed theory of concurrent large swelling and finite-strain plasticity is used to co-evolve fields of stress, deformation, concentration of lithium, and chemical potential of lithium. We identify three types of behavior. When the yield strength is high and the charging rate is low, the entire particle deforms elastically in all cycles. When the yield strength is low and the charging rate is high, the particle (or part of it) undergoes cyclic plasticity. Under intermediate conditions, the particle exhibits the shakedown behavior: part of the particle flows plastically in a certain number of initial cycles, and then the entire particle remains elastic in subsequent cycles. We discuss the effect of the three types of behavior on the capacity and the electrochemical efficiency.